Transcript population of units

Math 250
Introduction to Probability
and Statistics I
What is Statistics?
Statistics as a subject provides a body of
principles and methodology for
• designing the process of data collection
• summarizing and interpreting the data
• drawing conclusions and generalities.
Figure 1.1 (p. 2)
Gallup Opinion Index
Statistics in our everyday life
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Employment data
Consumer price index
Gallup poll
Quality and productivity improvement
Testing medicines
Population and Sample
A complete set of data is either physically impossible or from
a practical standpoint not feasible (limitations of time,
resources, facilities).
• A unit is a single entity, usually a person or an object,
whose characteristics are of interest.
• The population of units is the complete collection of units
about which information is sought.
• A statistical population is the set of measurements (or
record of some qualitative trait) corresponding to the entire
collection of units.
• A sample from a statistical population is the subset of
measurements that are actually collected.
Table 1.1 (p. 9)
Populations, Units, and Variables
How to select a sample?
• Must be impartial and objective
• Samples consisting of responses to call-in requests
will, in general, not be representative of the
population.
• The name of each unit written on a separate slip of
paper and the slips placed in a box; slips can be
drawn one at a time without replacement
• Using a random number table to select a sample
Table 1.2 (p. 12)
Random Digits: A Portion of Table 1, Appendix B
Collection of Data
Before collecting data
• Develop a statement of purpose that is both
specific and unambiguous.
(e.g., is the water safe for swimming)
• Translate the purpose into a measurement or
a qualitative trait.
(e.g., the amount of a radioactive material in
water doesn’t exceed a certain safe limit)
Objectives of Statistics
The major objectives of statistics are:
1. To make inferences about a population from an
analysis of information contained in sample
data. This includes assessments of the extent of
uncertainty involved in these inferences.
2. To design the process and the extent of sampling
so that the observations form a basis for drawing
valid inferences.